I made so diggin' out little bit more and found something that could be true in your case also.
Now your site is on hosted server (IIS). Probably you have username and password to administer your webspace? And you have to login to do so (screenshot).
Now when you logon to that server (IIS) you give a username (eg. john) that have rights to that directory where your stuff exists and after you're logged on this user information is in IE's memoryspace.
This username is not the same one that server is using when its runnig php (as module or cgi) and this is where the errors appears. IE is giving the server that username information what is in it's memory and it tries to run those php's under that username and that username does not have right to run php.exe directly. (I hope somebody can actually translate this to common language ).
So this problem should not affect any of those potential visitors.
Now if shutting down the browser doesn't take away the problem, there might wrong settings in your browsers security settings ( tools -> Internet options -> Security tab -> Custom level button -> User authentication section).
I hope this helps you somehow, even a little bit.
- Janne -